By: Tim Bower

Applied Data Analysis and Tools Study Guide

This study guide is available from timbower.us.

This study guide is made available by the Creative Commons Attribution 3.0 United States License.

This Applied Data Analysis and Tools Study Guide provides notes and information for the Applied Data Analysis and Tools (ETB 310) course offered by K–State Salina, which is the campus of Kansas State University located in Salina, Kansas. Self study of the material in the Study Guide is welcome.

Contents:

• 1. Welcome to Data Analysis and Tools
  • 1.1. Introduction to the Course
  • 1.2. Weekly Schedule
  • 1.3. Attendace Quiz Hints
  • 1.4. Homework Hints
• 2. MATLAB Programming
  • 2.1. The MATLAB Development Environment
  • 2.2. Variables and Values
  • 2.3. MATLAB Scripts
  • 2.4. Input and Output
  • 2.5. For Loops
  • 2.6. Control Constructs
  • 2.7. Vectors and Matrices in MATLAB
  • 2.8. MATLAB Functions
  • 2.9. Functions Operating on Vectors
  • 2.10. Importing Data Into MATLAB
  • 2.11. Text Strings in MATLAB
• 3. Graphical Data Analysis
  • 3.1. Using the Plot Tool
  • 3.2. Basic Line Plots
  • 3.3. 3-D Plots
• 4. Statistical Data Analysis
  • 4.1. Introduction to Statistics
  • 4.2. Common Statistical Functions
  • 4.3. Moving Window Statistics
  • 4.4. Probability Distributions
  • 4.5. Generating Random Numbers
  • 4.6. Statistics on Matrices
  • 4.7. Plots of Statistical Data
  • 4.8. Central Limit Theorem
  • 4.9. Sampling and Confidence Intervals
  • 4.10. Statistical Significance
• 5. Using the Symbolic Math Toolbox
  • 5.1. Throwing a Ball Up
  • 5.2. Symbolic Algebra
  • 5.3. Symbolic Calculus
  • 5.4. Symbolic Differential Equations
• 6. Introduction to Linear Algebra
  • 6.1. Working with Vectors
  • 6.2. Working with Matrices
  • 6.3. Geometric Transforms
  • 6.4. Systems of Linear Equations
  • 6.5. Elimination
  • 6.6. LU Decomposition
  • 6.7. Cholesky Decomposition for Positive Definite Systems
  • 6.8. Linear System Applications
  • 6.9. Numerical Stability
  • 6.10. Orthogonal Matrix Decompositions
  • 6.11. Over-determined Systems and Vector Projections
  • 6.12. Under-determined Systems
  • 6.13. Left-Divide Operator
• 7. Least Squares Regression
  • 7.1. Linear Regression
  • 7.2. Quadratic and Higher Order Regression
  • 7.3. polyfit function
  • 7.4. Goodness of a Fit
  • 7.5. Generalized Least Squares Regression
  • 7.6. Fitting Exponential Data
• 8. Application of Eigenvalues and Eigenvectors
  • 8.1. Introduction to Eigenvalues and Eigenvectors
  • 8.2. Eigenvector Animation
  • 8.3. Finding Eigenvalues and Eigenvectors
  • 8.4. Properties of Eigenvalues and Eigenvectors
  • 8.5. Diagonalization and Powers of A
  • 8.6. Change of Basis and Difference Equations
  • 8.7. Systems of Linear ODEs
• 9. Singular Value Decomposition (SVD)
  • 9.1. The Geometry of the SVD
  • 9.2. The Classic SVD
  • 9.3. How SVD Changes Vectors
  • 9.4. Dimensionality Reduction
  • 9.5. Fundamental Matrix Subspaces
  • 9.6. Other Applications of the SVD
• 10. Principal Component Analysis (PCA)
  • 10.1. PCA for Data Analysis
  • 10.2. PCA for Clustering
  • 10.3. PCA for Recognition
• 11. Computational Numerical Methods
  • 11.1. Optimization
  • 11.2. Data Interpolation
  • 11.3. Numerical Differentiation
  • 11.4. Numerical Integration
  • 11.5. Numerical Differential Equations
• 12. Orthogonal Matrix Factoring
  • 12.1. Introduction
  • 12.2. The Unitary Transformation Matrices
  • 12.3. The Saga of the Eigenvalue Problem
  • 12.4. The Solution to the Eigenvalue Problem
  • 12.5. Calculating the SVD with Unitary Transformations
• 13. Appendix
  • 13.1. Norms
  • 13.2. Vector Spaces
  • 13.3. Finding Orthogonal Basis Vectors
  • 13.4. Linearly Independent Eigenvectors
  • 13.5. All About the Number e
  • 13.6. A Matrix Exponent and Systems of ODEs
• 14. Homework
  • 14.1. Entering Basic Equations
  • 14.2. Fourier For Loop
  • 14.3. Save Your Money
  • 14.4. Practice with Vectors and Functions
  • 14.5. Element-wise Arithmetic
  • 14.6. Working with Tables
  • 14.7. The Flight of a Home Run Baseball
  • 14.8. Temperature Data Project
  • 14.9. Symbolic Math
  • 14.10. A Change of Coordinate Frames
  • 14.11. Matrix Homework
  • 14.12. Rectangular Systems Homework
  • 14.13. Projection of Static Force Vectors
  • 14.14. Least Squares Regression Homework
  • 14.15. Eigenvalue / Eigenvector Homework
  • 14.16. System of Linear ODEs Homework
  • 14.17. Markov Matrix of Land Use
  • 14.18. PCA Data Classification
  • 14.19. Numeric Methods Homework
• 15. Bibliography

Indices and tables

• Index
• Search Page